Visit our Christmas Gift Finder
Probabilistic Number Theory II: Central Limit Theorems - Grundlehren der mathematischen Wissenschaften 240 (Paperback)
  • Probabilistic Number Theory II: Central Limit Theorems - Grundlehren der mathematischen Wissenschaften 240 (Paperback)
zoom

Probabilistic Number Theory II: Central Limit Theorems - Grundlehren der mathematischen Wissenschaften 240 (Paperback)

(author)
£79.99
Paperback 375 Pages / Published: 07/12/2011
  • We can order this

Usually dispatched within 3 weeks

  • This item has been added to your basket
In this volume we study the value distribution of arithmetic functions, allowing unbounded renormalisations. The methods involve a synthesis of Probability and Number Theory; sums of independent infinitesimal random variables playing an important role. A central problem is to decide when an additive arithmetic function fin) admits a renormalisation by real functions a(x) and {3(x) > 0 so that asx ~ 00 the frequencies vx(n;f (n) - a(x) :s;; z {3 (x) ) converge weakly; (see Notation). In contrast to volume one we allow {3(x) to become unbounded with x. In particular, we investigate to what extent one can simulate the behaviour of additive arithmetic functions by that of sums of suit- ably defined independent random variables. This fruiful point of view was intro- duced in a 1939 paper of Erdos and Kac. We obtain their (now classical) result in Chapter 12. Subsequent methods involve both Fourier analysis on the line, and the appli- cation of Dirichlet series. Many additional topics are considered. We mention only: a problem of Hardy and Ramanujan; local properties of additive arithmetic functions; the rate of convergence of certain arithmetic frequencies to the normal law; the arithmetic simulation of all stable laws. As in Volume I the historical background of various results is discussed, forming an integral part of the text. In Chapters 12 and 19 these considerations are quite extensive, and an author often speaks for himself.

Publisher: Springer-Verlag New York Inc.
ISBN: 9781461299943
Number of pages: 375
Weight: 611 g
Dimensions: 235 x 155 x 21 mm
Edition: Softcover reprint of the original 1st ed. 198

You may also be interested in...

Elementary Number Theory
Added to basket
The Man of Numbers
Added to basket
£18.99
Hardback
A Mathematical Tapestry
Added to basket
A Comprehensive Course in Number Theory
Added to basket
Euclid's Elements
Added to basket
£31.99
Hardback
The Irrationals
Added to basket
£14.99
Paperback
Numbers: A Very Short Introduction
Added to basket
The Theory of Algebraic Numbers
Added to basket
Elliptic Tales
Added to basket
£13.99
Paperback
As Easy As Pi
Added to basket
£6.99
Paperback
Proofs from THE BOOK
Added to basket
Euclid's Elements
Added to basket
£21.99
Paperback

Please sign in to write a review

Your review has been submitted successfully.